Why are experimental studies important in psychology?

One answer is that empirical evidence is important for any empirical science, of which (part of) psychology is an instance. Initially theories in psychology came from introspection, and often initially received little support because of the limits of introspection. Surprising results from emprical studies generate the most interesting theories.

Psychology is still a very young science with many important social implications, for instance related to how to help people with mental health problems, how best to select people for jobs, helping people to improve how they learn and make decisions. The only way to put serious psychological theories to the test is by empirical study. If a result replicates, and supports a theory, then this offers a reason to believe in the theory.